To minimise the risk components determined in the previous section, we require portfolios on the Capital Market Line.
$$\mu_p = r_o + \dfrac{\mu_m – r_o}{\sigma_m} \cdot \sigma_p$$
The CAPM also says
$$\mu_p = r_o + \beta_p(\mu_m – r_o)$$
By comparing the two equations above,
\begin{align}\beta_p &= \dfrac{\sigma_p}{\sigma_m}\\ \\
\Rightarrow \; \sigma_p^2 &= \beta_p^2 \sigma_m^2 \end{align}
Comparing this with the result for $\sigma_q^2$ in equation $(7)$ of Risk Components of the CAPM Model, this tells us that
portfolios on the Capital Market Line have no specific risk
Importantly, this means that fund managers must diversify as there is no reward for portfolios on the capital market line since there is no specific risk with such portfolios.
<!–more–$$\qquad \Bigg( \beta_p = \dfrac{\rho \sigma_p \sigma_m}{\sigma_m^2} \Bigg)$$ >